"Each pixel represents the state of the 4 cells of 4 cellular automata, which are cross coupled and have their individual state transition tables. There is a "history" or "memory" of the previous states which is used as an offset into the state transition tables, resulting in update rules which depend on what has happened at that pixel in previous generations. Different regions end up in a particular state or cycle of states, and act very much like immiscible liquids with surface tension."

Tuesday, December 13, 2011

John Conway's Game of Life is a cellular automaton in which randomized cells evolve according to a fixed set of rules. Usually this evolution appears as an animation, here we see the evolution through time in a still image, with height from top to bottom corresponding to subsequent generations of cells.

The Catalan numbers are a sequence of numbers, much like the Fibonacci numbers, which are given by the equation

Like the Fibonacci numbers, they too pop up all over the place, for example, the Catalan numbers correspond to the number of ways a regular n-gon can be divided into n-2 triangles.
Above is a visualization of the Catalan numbers.

Pictures of Math

Math can be incredibly beautiful. Often this beauty is only accessible to those who study math at an advanced level; images such as these have a universal aesthetic.

I started this blog hoping to share some of the more colorful parts of mathematics with those who may have dismissed math as the result of a bad algebra or calculus class. Meanwhile, for the mathematically minded, I hope these images inspire you to learn new things.

With every image posted, there are links so that you can read more about the mathematics behind the image. I encourage you to do so as sometimes, the math involved is just as beautiful, if not more so.